Pi Definition and 514 Threads

Not actually a HW question, but, is there a quick explanation that could show why: \pi = 16\arctan(\frac{1}{5}) - 4\arctan(\frac{1}{239}) I read that somewhere, and it turned out to be true, so I was just wondering how that came about...

Since one can construct the length of a non-integer square root by drawing accurate triangles, and can draw a circle with a circumference of pi, then shouldn't one be able to plot corresponding non-integer square roots and pi on a number line? I know these numbers are supposedly irrational, but...

Hiya, I'm having trouble finding a simple proof for gamma of 1/2 = root pi? Any suggestions

Could somebody please explain the 2-fold degenerate sigma 2p is lower in energy than that of 4-fold degenerate the pi 2p bondings state in the O2 molecule? Does it have anything to do with resonance energies perhaps?

I saw the other thread, but figured this question was sufficiently distinct to warrent a new thread I was recently looking at this series \[ \sum_{n=1}^\infty \frac{1}{n^{2}} = 1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \cdots + \frac{1}{n^{2}} = \frac{\pi^{2}}{6} \approx 1.645 \] My...

How was the irrational number pi invented or how did man reach upon it? I have studied elementary calculus to understand the basic kinematics. In fact I know only the formulae to find for integration and derivative of some standard functions. The limits and such things weren't taught to me. It...

Pi does anyone know the exact number to pi (yes the one over 1000 characters long:P) i need it a.s.a.p

how to plot the irrational number pi on a number line. i know the procedure for square roots of different non-perfecr square number. it is by drawing a perpendicular at a suitable integral length again at suitable integral length such that the hypotenuse is of required length as per the...

I recently though it would be kewl to remember pi up to 256 digits :rolleyes: Ok, I am a little wacko. My original idea was to remember 1 digit per day. But in the last three days, I have already memorized the first 18 digits. I couldn't help but look. In any event, what would be the...

Hi I have to draw a Feynman diagram for the following reaction: K^{*+} \rightarrow K^0 + \pi^+ The K^{*+}-meson is composed of an u and an anti-s quark, the K^0-meson is composed of a d and an anti-s quark, and the \pi^+-meson is composed of an u and an anti-d quark. I have drawn...

Maple Help! could anyone tell me how to use the function pi in maple. http://en.wikipedia.org/math/e66964312bccf80023e4815edd53a542.png i need to figure it out for a statistical mechanics assignment. Thanks

Has anyone ever seen this movie? It really is not all that great, and in one scene the main character, which is a mathmatician, is describing the number phi and the logarithmic spiral, but for some reason he calls it theta instead of phi. I don't know if that is completely incorrect, or if...

Am I crazy or this is impossible to do if we require that the period of the extended even function be 2pi ? Yet, this question comes in my textbook before the section concerning Fourier extension of functions of period other than 2pi. So there must be a way?

My son's computer science teacher claims that there is no way to devise a computer algorithm that can generate a truly random sequence of numbers (only a pseudo-random sequence that ultimately repeats). Yet there are algorithms with a finite number of steps that generate the decimal digits of...

About 20 years ago I caught an article about a graduate student who had found an algoritm which would return the n-th digit of \pi without needing to compute the preceding digits. In other words you could ask for the 812th digit of \pi and it would spit it out without computing the...

Has a name been given to this constant? The most I've seen is calling it k, but is there another name for it, or any statement for understanding its meaning (such as how e0 can be called the "permittivity of vacuum")?

almost everyone has heard of the Bible code. what about the pi code? predicting the future with the Pi code! infinite digits means all possible combinations, right? if you get bored one day, you can predict the future.

It's a happy day :biggrin: Today is pi approximation day. The date, written in day/month format, is 22/7. I doubt the celebration will be quite as extravagant as the pi day of 1592 - March 14, 1592 at 6:53:58 (3/14/1592 6:53:58) touched off one the great celebrations in man's history. I...

OK, I can't stand it any more. This is a Public Service Announcement. The ratio of the circumference of a circle to its diameter is called pi, not pie. OK, here's a small demonstration just to clarify: This is pi: http://www.ualr.edu/~lasmoller/mathresources/bigpi.gif This is pie...

pi is the ratio of circumference to diameter.That is true in a flat, Cartesian space. In a curved space, a physicist measuring the ratio of the circumference of a circle to its diameter will come up with a different value, which will be more or less than pi depending on which way his space is...

Pi is said to be discovered by ancients, but if even we don't know the EXACT number of pi, how could they, or was theirs just a close estimate of pi?

I haven't been able to prove: ln(e)/e > ln(pi)/pi without calculating any of the values. Help would be much appreciated.

pi bonds for hybridizations, yes/no questions im having a bit if trouble with this but i need to know the number of pi bonds for the sp^3, sp^2 and sp hybridizations thanks if you can help ^^ i have another question as well,there are some questions and they have yes or no answers but I'm...

A problem in my textbook guides you through this proof using a multiple integral. I follow the whole thing except for one step. It requires that you show that (sorry don't know latex, I(a,b) will denote integral from a to b, e the exponential) [I(-x,x)e^(-u^2)du]^2=I(R)e^(-u^2-v^2)dudv...

In what way can i calculate PI and output the result to the screen ? I heard from my friedn that MC method is good but is there any other ways to do that ? also, how many decimal digits am I able to output the result ? Thank you in advance -KMCB1234

I was wondering if there are any formulations of Pi or e that use "n-euclid space" to approximate it? Or really just the use of any linear algebra to approximate Pi or e? Thanks... Derek Mohammed

How do we know pi to so many decimal places? How can that be determined so precisely? http://wikisource.org/wiki/Pi_to_1%2C250%2C000_places

This was brought to my attention today, and I haven't had much time to think about it; I think it has something to do with fractals. If you have half a circle with diameter of 2, the circumference will be \pi. If you create two circles, each with diameter of 1, the combined length of the...

How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard

\cos \theta = \frac {2} {3} and \frac {3\pi} {2} <\theta<2\pi then determine the exact value of \frac {1} {\cot\theta} I did this question using sin^2+cos^2=1 subbing in cos and then solving for sin when i got both values i realized that 1/cot theta = tan theta which is (sin theta)/(cos...

does anyone know what the symbol that looks like a tall pi means?

In ammonia, why the N atom is sp3 hybridized and not sp2 hybridized...since there are only 3 bondings... Also, in ethyne, that is H-C(triple bond)C-H...for the formation of 2 pi bonds, why it is the unhybridized 2px orbital and 2py orbital of each C atom overlap with each other? How about the...

If Pi is continual and random-digited as scientists say, then how could it be the quoteint of the circumference and the diameter, because any thing that includes a fraction cannot be continual and random digited. The only explanation that keeps Pi continual and random digited is that the...

Lads, I'd be glad if you were able to take a view of the last developments in the thread https://www.physicsforums.com/showthread.php?t=46055 and see if you can do some suggestion, as we have a pi^2 expresion which should somehow be related to integer pythagorean triples.

Pi can be exact if we have a new number system. :mad:

Supposedly Pi has infinite and random digits. Therefore pi cannot be a fraction unless the top numeber or the bottom number is a number with infinite and reapiting random digits. so therefore the diameter or the circumference must always be a infinite and random digited. BUT, this isn't true. if...

Plus c and h, of course. The idea is to collect here in only a thread all the approximations voiced out during the summer. Surely this is to be quarantinised in TheoryDev, but it is interesting enough to be kept open as a thread (if closed, please be free to use my...

PI: More mokeys with Typewriters!? There exists a recent post on the subject of an infinite amount of monkeys doing a lot of typing. You know the premise. I was going to post this there, but figured it might deserve to be a new thread altogether. There's this number- Pi: 3.14159... and off...

This is by far the most exciting site on pi and phi I have ever seen. You must see this. http://goldennumber.net/five(5).htm Don't forget to see the side links to other pages in the site that describe other interesting facts.

My dad and I got in an argument about accuracy of pi values. He said that the ratio 22/7 will always be more accurate than any decimal value of pi. I said that the value 3.14159265358979 is much more accurate. I'm 100% certain that I am correct, but I can't really think of how to prove this...

This is more of a dimensional analysis or unit analysis problem than a basic analysis problem. So if I didn't post this thread in the right forum, please delete it. Moving on, I'm having trouble grasping the concepts behind the Buckingham Pi Theorem. After reading some textbooks and doing...

How would I go about defining pi (and using) as 3.1415926535897932384626433832795? I've tried using double, long double and #define pi 3.1415926535897932384626433832795 but it, instead, takes 3.14159. Is there any way to get it more accurate?

pi miscalculated or not irrational? I know that computers have calculated thousands of digits of pi, but does this mean that pi is an irrational number? How can we be so sure that it is irrational? And I have one more question. The circles we see in real life are not perfect circles. Does this...

Im looking for some proofs on the rationality of pi. I also want to know what some people think about it.

:smile: Hi ! I was pondering over the morphology of etymology, and the tonal "Aum" or "OM" of the vedic sanskrit. If you look at these tones in a cymatic (wave theory) way, you discover some unqiue principles. All of our time we have spent trying to create pi...

The square root of pi is 1.777245... I know. But my math teacher says its impossible to determine a square root of an irrational number. Can anyone shed any light on this? is it or is it not possible to determine the square root (or any root) of an irrational number?

what does pi mean, and where did it come from, i know its 3.141592654, but i also know there's a lot more decimal places then that, does anyone know anything about it?

A beam of charged pi-mesons is traveling with a speed of v=0.3c. The mean life of a pi-meson is 2.6 x 10^-8s. What is the mean distance traveled by a pi meson before it decays? How do u do this?

is this correct -(pi) + (1 - 2i)((pi)^2) = i^2 i = (-1)^(1/2) (pi)= 3.142... peace :redface:

I'm doing this paper on pi and the question popped up in my mind: why is pi interesting to us? ok, it might be interesting to find new, faster ways to calculate it and stuff like that, but does it have any use, function? what progress are we making? I know it's ralated to the strings in the...